I've often wondered if it is somehow a mistake for mathematics to distinguish between i and -i. There is absolutely no mathematical way to distinguish between the two. Perhaps they should only be referred to as a pair, and never one at a time? Opinions? --Dan P.S. In a faintly related vein, if we define i^z := exp(pi*z*i/2), then iterating this function on the starting value of z = i approaches a limit L of approx. 0.6528812343931018 + i 0.3675743023883531 (or so says my C program). Hmmm, Mathematica seems to give a rather different answer. (Can someone please recompute; my program iterated i^z on the starting value z = i forty times before the new value was within 10^(-9) of the last one, but maybe my computation was done in by roundoff error.) In any case: 1. Is it possible that this limit L of towers of exponentiated i's can be identified as some familiar number? 2. In any case, what can be said about its number-theoretic properties? (In a sense L^(1/L) = i, so apparently Gelfond-Schneider implies L can't be an algebraic irrational.) --Dan